The Brown family has many pairs of athletic shoes. They counted $p$ pairs all together. They decided to give away $6$ pairs, because they had outgrown them. After giving $6$ pairs away, the Brown family still has $11$ pairs of athletic shoes remaining. Write an equation to describe this situation. How many pairs of shoes did the Brown family start with?
The Brown family had ${p}$ pairs of athletic shoes. They gave away ${6}$ pairs. After giving some shoes away, they have ${11}$ pairs remaining. We can represent the number of pairs of athletic shoes that the Brown family has remaining as a difference: ${p} - {6}$ We know that they have ${11}$ pairs of shoes remaining. We can set these two expressions equal to describe this situation with an equation: ${p} - {6} = {11}$ Other ways to represent the situation with an equation include: ${11} = {p} - {6}$ or $ p = 6 + {11}$. Now we can solve for ${p}$. Add ${6}$ to both sides of the equation to get ${p}$ by itself: $\begin{aligned} p -{6} +{6} &= {11}+{6} \\ \\ {p} &={17} \end{aligned}$ The following equation matches this situation: $p - 6 = 11$ The Brown family started out with $17$ pairs of shoes.